Assessment of Adsorptive Filter for Removal of Formaldehyde from Indoor Air

We varied face velocities and initial formaldehyde concentrations to investigate the formaldehyde removal performance of coconut shell activated carbon (AC) adsorptive filter media. AC surface were rather uneven, with coarse and small pores, and with amorphously formed irregular layer structures. C, O, Mg, P etc. were detected, which showed the existence of MgO in AC. The AC surface area was 1333.3304 m g, and ketone -C=O bonds were successfully grafted onto the carbon. At any given face velocity, the experimental results indicate that the adsorption capacity increased and the breakthrough time decreased as the initial concentration increased. The breakthrough behavior of the AC adsorptive filter could henceforth be evaluated with confidence using the breakthrough curves predicted by the Yoon-Nelson model. Of the three kinetic models that were assessed, the experimental and calculated results show that the correlation coefficient and mean absolute performance error (MAPE) of the pseudo-second-order model generated the best approximation of the kinetic dynamics of the adsorption process—better than those of the pseudo-first-order model and intraparticle diffusion model. Both the intraparticle diffusion model and the membrane diffusion affected the overall rate of the adsorption process by more than one step. The equilibrium data of the AC adsorptive filter media was found to best fit the Langmuir model. The D-R equation predicted the equilibrium capacity of AC at a relative pressure of 0.151.


INTRODUCTION
Human beings typically spend more than 90% of their waking hours in indoor environments.As such, pollutants found in indoor air may in many cases represent a higher hazard to human health than those present in the outdoor environment (Brunsgaard et al., 2012).Recent changes to building regulations have demanded much higher airtightness requirements for residential and commercial buildings for reasons of improved energy conservation.As a result, there exists the potential for increased concentrations of volatile organic compounds (VOCs) within indoor environments.The negative impact on health and well-being and comfort (Chuck and Kim, 2013) of occupants in air-tight housing is well documented.Among VOCs, formaldehyde (HCHO) has long been established as a hazardous and harmful substance (Mui et al., 2008).The primary source of formaldehyde found as a pollutant in indoor air is pressed wood products manufactured using urea formaldehyde resins (U.S. Consumer Product Safety Commission, 2015).
There are several studies on air cleaning technologies for indoor formaldehyde removal.UV photolysis is limited due to its trend to produce ozone and radicals with harmful effects.Photocatalytic oxidation has been utilized for ppm levels of contaminant degradation and ppbv concentrations need to be measured, and their main deficiencies are the short lifetime of the catalyst and the creation of harmful by-products.Cold or non-thermal plasma are not yet on the market (Luengas et al., 2015).These major technical issues also have limitations like high energy consumption and low removal efficiency (Gilbert et al., 2008;Mo et al., 2008).Biological degradation (Lu et al., 2012) and botanical air filtration are still under development, currently operating at low efficiency and with insufficient understanding of long-term safety (Wang et al., 2014;Luengas et al., 2015).At this time, neither of these techniques is broadly employed for indoor pollutant removal (Lu et al., 2012).Activated carbon adsorption is a simple, effective, and low cost method to reduce the concentrations of formaldehyde removal in indoor air (Lu et al., 2015).
The primary purpose of this study characterized the physical and chemical properties of the AC by Scanning electron microscope (SEM), X-ray diffraction (XRD), Energy Dispersive X-ray Spectroscopy (EDS), Brunauer-Emmett-Teller (BET), and Fourier transform infrared spectroscopy (FTIR) analysis to investigate the equilibrium, breakthrough behavior, and the applicable assessment of three kinetic models: pseudo-first-order, pseudo-secondorder and intraparticle diffusion.The latter assessment was conducted under various experimental conditions using the correlation coefficient (R 2 ) and the mean absolute percentage error (MAPE) to characterize the kinetic data.As a result, this study provided the essential parameters to consider when designing and operating an adsorptive purifier for removal of formaldehyde from indoor air, and implementing strategies to improve air quality in the indoor environment.

Adsorptive Capacity
This study used the testing method of VanOsdell et al. (1996) shown in Fig. 1.The mixed air passes through the adsorbent.Removal efficiency (η) was calculated with the initial concentration (C 0 ).Adsorption capacity (q t ) is defined as follow (Shiue et al. 2010

Breakthrough
Generally, it is not practicable to measure activated carbon filter breakthrough time against formaldehyde concentration in real indoor environments.When the outlet concentration reached 2% of the initial concentration, the breakthrough time was determined (Dehdashti et al., 2011).While changing only formaldehyde concentration, simplified breakthrough time estimation is shown as (Cheng and Tsai, 2007;Cheng, 2008;Shiue et al., 2010): where t b is the breakthrough time, C 0 is the initial (inlet) concentration of adsorbate (ppmv), α is the constant.Eq. ( 2) predicted the performance of the activated carbon filter.Yoon and Nelson (1984) initially developed a simple model that proposed the rate of decrease in the probability of adsorption for each adsorbate molecule is proportional to the probability of adsorption of an adsorbate (P ads ) and the probability of breakthrough of the adsorbate (1 -P ads ): ( 1) Integrating Eq. ( 3), and defining τ as the time required for 50% breakthrough (i.e., P ads = 0.5, hereinafter referred to as the stoichiometric breakthrough time): where k′ is a rate constant, C t is the breakthrough (effluent) concentration of adsorbate.The calculation of theoretical breakthrough curves for a single-component system requires the determination of the parameters k′ and t for the adsorbate of interest.
In accordance with Eq. ( 4), the value of k′ can be got from the slope of the plot ln[C t /(C 0 -C t )] versus breakthrough time t, and the value of t (50% breakthrough time) can be decided as the time at Q = 0.5 (i.e., C t = C 0 /2).Applying k′ and t of Eq. ( 4), one may cause the complete breakthrough curve for a given set of experimental conditions.Furthermore, Yoon and Nelson (1984) have proposed the following equation: where K is a proportionality constant for a given adsorbate and determined type of adsorbent.Both k′ and t alternatively rely on the concentration of the adsorbate and the face velocity.

Kinetic Model
The pseudo-first-order equation is expressed by Lagergren equation (1898) as follows: where q e is the amount of adsorbed formaldehyde per unit weight of adsorbent, q t is the amount of adsorbate adsorbed at time t.
The pseudo-second-order model is shown as (Ho and McKay, 1999): The intraparticle diffusion model is described as follows (Guibal, 1998): Error Analysis Mandal et al. (2015) used correlation coefficient (R 2 ) and mean absolute performance error (MAPE) values to verify the experimental data for the most suitable kinetic model.These expected indices were computed by utilizing the following equations: exp 1 exp 1 100 where q pre and q exp are the expected and measured values of formaldehyde concentration, respectively; q ̅ illustrates the average values of related q; n is the total number of observations.

Adsorption Isotherm Model
Between adsorbed and free formaldehyde in air, the equilibrium is given by the linearized Langmuir isotherm model as per the following equation (Cheng and Tsai, 2007;Bernabe et al., 2015): where q e is the adsorbed amount of formaldehyde per unit weight of adsorbent at equilibrium; C e is concentration of free formaldehyde in air; q max is maximum adsorption capacity; and K L is the Langmuir's adsorption equilibrium constant related to the affinity of the binding sites; this phenomenon has been described before (Cheng and Tsai, 2007;Bernabe et al., 2015).
Linearizing the Freundlich isotherm model is shown as (Cheng and Tsai, 2007;Bernabe et al., 2015): where k F and n are Freundlich constants, which related to the adsorption intensity and adsorption capacity, respectively (Cheng and Tsai, 2007;Bernabe et al., 2015).The Dubinin-Radushkevich (D-R) equation, which was initially formulated from the Polanyi adsorption potential theory and represents molecular adsorption as a pore-filling phenomenon rather than a layer-covering one, has been used to correct the Freundlich isotherms (Yao et al., 2009).In accordance with the D-R equation the adsorption capacity (W), expressed as the adsorbed liquid volume per unit mass of adsorbent, is related to the adsorption potential (A) as given by (Dubinin, 1966): and where W is the volumetric adsorption capacity, W 0 is the maximum adsorption space, k is the parameter for each system of adsorbate and adsorbent, A is adsorption potential, R is the universal gas constant, T is the absolute temperature, P 0 is the saturated vapor pressure at temperature T, and P is the partial pressure of the adsorbate.Combined Eqs. ( 13) and ( 14), the gas-phase partial pressure related to the adsorption capacity as follows:

Experimental Methods
The 2.2 mm thickness AC-loaded nonwoven fabric filter media (provided by AIRREX Co. Ltd.) was placed into a 10 cm × 10 cm testing rig located in a temperature of 28 ± 1°C by ambient air-conditioning system.The testing airflow was controlled at relative humidity (RH) of 40 ± 2% by adjusted primary split airflow.The characteristics of fabric filter media and schematic test system diagram are shown in Table 1 and Fig. 2, respectively.
The face velocity of filter media was rated at 0.25, 0.5, and 0.75 m s -1 (VT110-VT115 Hotwire Thermo-anemometer).A source of compressed air was first passed through a drier, adsorbent, and high efficiency particulate air (HEPA) filter to generate a "zero air."This zero air was then blended with formaldehyde via a gas-generator to produce the challenge gas entering the test rig (Fig. 1).99.9% grade formaldehyde solvent was filled into the gas-generator and submerged in a water bath (temperature adjustable from 15°C to 25°C).The formaldehyde entered upstream of the testing rig, controlled by passing air through a mass flow controller (Fujikin T1000).Formaldehyde concentration was fixed at 0.25, 0.56 and 0.79 ppm with ±2% deviation.A real-time formaldehyde analyzer (Formaldemeter htv-m) monitored the concentration of the challenge gas.
Essential) was used to study the surface morphology of the adsorbent.X-ray diffraction (XRD) is for chemical characteristics and surface morphology of adsorbent study.Energy-dispersive X-ray spectrometry (EDS, ZEISS ΣIGMA Essential) was employed for the elemental analysis of the sample.To obtain an infrared spectrum of absorption or emission of adsorbent, Brunauer-Emmett-Teller (BET, Micrometrics ASAP2020) method was used to study the surface area.Fourier-transform infrared spectra (FTIR, Spectrum one) was applied.

Characterization
Scanning Electron Microscope Fig. 3 shows the SEM image of AC under different magnification (100, 400, and 2000) magnification.Fig. 3(a) indicated the surface is smooth and distributed with small pores.Moreover, it can observe a little crack and tiny particle near the pore.From Figs. 3(b) and 3(c) the surface of AC is rather uneven, coarse and porous.The shape is columnar and lamellar on the surface because the coconuts have the cellulose sintering at high temperature.

X-Ray Diffraction (XRD)
Fig. 4 indicated XRD pattern of AC.The graph was observed that AC is amorphous.The two broad Bragg or diffraction peaks were shown around 22° and 43° indicated that the crystallites were produced by two or more of these plates layer being stacked one above the other.Irregular layer structure were formed the amorphous that the XRD diffraction peaks were broad.

Energy Dispersive X-Ray Spectroscopy (EDS)
Fig. 5 illustrated the EDS detection area of AC; element such as C, O, Mg, P etc. can be found in the AC.AC is composed of C, O, and P accounting for 77.48%, 18.71%, 3.28% respectively.And we can calculate the O/C ratio = 24.14%which means around 1.0 unit carbons are given by 24.14 unit oxygen.Some metal element like Mg with weight percentage 0.28%.Mg and P are detected in the elemental analysis of AC.The EDS analysis showed that the Mg/C ratio = 0.68%, which further proves the existence of MgO in the coconut's activated carbons.

Surface Area and Pore Size
The BET analysis showed that the surface area was 1333.3304m 2 g -1 after BET analysis.The identified data showed that micropore volume of AC is 0.13 cm 3 g -1 , meso volume is 0.45 cm 3 g -1 , total volume is 0.840442 cm 3 g -1 ; BJH adsorption average pore diameter is 2.21361 nm in the range of 2.0-3.0 nm.The most important thing is the area between adsorption linear and desorption linear in Fig. 6.

Fourier-Transform Infrared Spectra
Fig. 7 shows FTIR spectroscopy in analysis of the functional groups.AC depended upon the experiments with molecular organic compounds that we can list the orders of  the absorptive bands.It showed an intensive band 3417 cm -1 has been explained by stretching of ketone -C=O bonds.A weak strength bonding at 2329 cm -1 indicated the formation of O-H bonds from carboxylic acid (Boehm, 2002).Near 1166 and 1086 cm -1 has been explained by reverse stretching vibrations of carboxylic acids C-O bonds.

Adsorption Capacity
Fig. 8 presents variations in formaldehyde adsorption capacity with different inlet concentrations at different face velocities.Equilibrium time (t t ) is defined as the time when the outlet concentration is 98% of the inlet concentration.The proportional relationship between natural logarithm of equilibrium time and formaldehyde adsorption capacity (Q) is presented as the formula (Scahill et al., 2004) in Table 2.These results are in agreement with Shiue et al. (2010) (flow rate of 0.076-0.152m s -1 at an inlet toluene concentration of 10-70 ppm).As shown in Fig. 8, if the inlet concentration of the adsorbate is increased, resulting in increased velocity of diffusion into the pores of AC, adsorption may reach equilibrium faster; the equilibrium time decreased from 86 to 30 min, 64 to 24 min and 46 to 12 min, while adsorption capacity increased from 0.265 to 0.2991 mg g media -1 , 0.3244 to 0.4726 mg g -1 , and 0.4726 to 0.6019 mg g -1 at 0.25, 0.5 and 0.75 m s -1 face velocities, respectively.

Breakthrough
Complete breakthrough is specified as the point at which the measured formaldehyde concentration at the outlet equaled its inlet concentration.Breakthrough was executed by varying initial formaldehyde concentrations from 0.25 to 0.79 ppmv at 0.25 to 0.75 m s -1 face velocity shown in Fig. 9.The breakthrough time was decreased from 78, 68, and 44 to 34, 28, and 14 min for 0.25 to 0.79 ppmv formaldehyde initial concentrations at 0.25 to 0.75 m s -1 face velocity, respectively.This phenomenon has been described before (Cheng andTsai, 2007, Jo andChun, 2014).Additionally, the breakthrough behavior also was decreased from 78, 68, and 34 to 44, 28, and 14 min for 0.25 to 0.75 m s -1 face velocity at formaldehyde initial concentration of 0.25, 0.56 and 0.79 ppmv, respectively.
The relationships between various logarithmic formaldehyde initial concentrations and various logarithmic breakthrough times are expressed in Fig. 10 and Table 3.The slopes of the lines were smaller for the formaldehyde with lower face velocity at the same concentration.The plots of Eq. ( 4) at various face velocities (Fig. 11) yielded linear curves with excellent correlations, the endpoint of the regression analyses used 50% breakthrough, i.e., ln(c b /c i -c b = 0).Table 4 listed the values of the slopes (k′) and the intercept of (-k).Both k′ and τ are dependent on the adsorbate inlet concentration.The rate constant k′ increased with increasing formaldehyde inlet concentration, as the stoichiometric breakthrough time τ decreased.Also, both k′ and τ were significantly affected by the face velocity; i.e., the value of k′ increased with increasing face velocity, while the value of τ decreased.Due to k′ and τ act in reverse trend, one would predict that k would be a constant with a well-behaved breakthrough times presented in Fig. 11.Certainly, as interpreted in Table 4, the value of proportionality constant K (2.60 ± 0.47) could be utilized as a basis of prevision for other hypothetical formaldehyde concentrations and face velocities.

Adsorption Kinetic Models
To determine the sorption mechanism, three common kinetic models, pseudo-first-order, pseudo-second-order, and intra-particle diffusion models, were applied to empirically analyze kinetic sorption data.

Pseudo-first-order Model
The plot of pseudo-first-order kinetics is shown in Fig. 12. Table 5 summarized the calculated constants according to the pseudo-first-order equation along with correlation coefficients (r 1 2 ).The adsorption amount q e,1 of formaldehyde increased from 0.264, 0.324, and 0.472 to 0.298, 0.502, and 0.601 mg g -1 for 0.25 to 0.79 ppmv formaldehyde initial concentrations at 0.25 to 0.75 m s -1 face velocity, respectively.It shows formaldehyde removal efficiency is dependent on initial concentration.In addition, the amount of formaldehyde adsorption decreased from 0.571, 0.787, and 0.986 to 0.291, 0.441, and 0.820 mg g media -1 for 0.25 to 0.75 m s -1 face velocity at 0.25, 0.56 and 0.79 ppmv formaldehyde initial concentration, respectively.The removal efficiency of formaldehyde is also dependent on face velocity.Moreover, the calculated data of q e,1 are closer to the experimental data.With the initial concentration increased from 0.25 to 0.79 ppm at face velocity 0.25 to 0.75 m s -1 , the rate constant (k 1 ) values were increased from 0.77 to 0.145, 0.082 to 0.227 and 0.125 to 0.547 min -1 , respectively.The rate constant (k 1 ) of the pseudo-first-order rate model is linearly related to formaldehyde initial concentration (C 0 ) is shown in Fig. 13.This result is similar to the findings of many previous studies (Saeid and Bahare, 2006).

Pseudo-second-order Model
Fig. 14 presents a plot of the pseudo-second-order kinetics for the formaldehyde adsorption onto AC filter media.Table 5 summarizes the calculated constants (k 2 ) of the pseudo-second-order equation along with correlation coefficients (r 22 ).The adsorption amount (q e,2 ) of the   formaldehyde increased from 0.309, 0.329, and 0.715 to 0.498, 0.785, and 0.721 mg g -1 media -1 for 0.25 to 0.79 ppmv formaldehyde initial concentrations at 0.25 to 0.75 m s -1 face velocity, respectively.The formaldehyde removal is based on initial concentration.In addition, the amount of formaldehyde adsorption q e,2 increased from 0.309, 0.402, and 0.498 to 0.35, 0.522, and 0.919 mg g -1 media -1 for 0.25 to 0.75 m s -1 face velocity at 0.25, 0.56 and 0.79 ppmv formaldehyde initial concentration, respectively.It shows that the formaldehyde removal efficiency is also dependent on face velocity.With initial concentration increased from 0.25 to 0.79 ppm at face velocity 0.25 to and 0.75 m s -1 , the rate constant (k 2 ) values were increased from 0.323, 0.4, and 0.409 to 0.715, 0.716, and 0.721 g mg -1 min -1 , respectively.Moreover, the calculated q e,2 values are closer to the experimental data, the rate constant (k 2 ) of the pseudo-second-order rate model related to formaldehyde initial concentration (C 0 ) is shown in Fig. 15.This result is similar to the findings of many previous studies (Saeid and Bahare, 2006).

Intraparticle Diffusion Model
Fig. 16 shows the plot of intraparticle diffusion model.The rate constants (k i ) are obtained from the slope of the  5.The adsorption process presented three steps: Stage 1: The adsorbate molecules are diffused in the adsorption and adsorbed on the outer surface (Shiue and Hu, 2012;Tang et al., 2016;Hu et al., 2017;Shiue et al., 2017).Stage 1 is finished before 2 min average at 0.25 to 0.79 ppm inlet formaldehyde concentrations of 0.25, 0.5, and 0.75 m s -1 face velocity, respectively.Stage 2: this stage is a developed process and k i is the highest, resulting that the intraparticle diffusion is the key controlling factor of adsorption rate (Shiue and Hu, 2012;Tang et al., 2016;Hu et al., 2017;Shiue et al., 2017).It kept and continues from 2 min to 25-49, 16-36, and 9-25 min of AC adsorptive filter media at 0.25 to 0.79 ppm inlet concentration of 0.25, 0.5, and 0.75 m s -1 face velocities, respectively.Stage 3: This stage is the adsorption equilibrium process, where the intraparticle diffusion further slows down, and the adsorption rate  decreases significantly due to the adsorbates almost filled the micropores and mesopores (Shiue and Hu, 2012;Tang et al., 2016;Hu et al., 2017;Shiue et al., 2017).

Error Analysis
The correlation coefficients of the pseudo-second-order kinetic model (average value = 0.969) is higher than the pseudo-first-order kinetic model (average value = 0.899) and the intraparticle diffusion model (average value = 0.863).This result is similar to the findings by Tsai et al. (2017) and Adelodun et al. (2016).For the adsorption process, physisorption might be the controlling mechanism by the highest correlation coefficient (average value = 0.969) and the lowest mean absolute percentage error value (average MAPE < 8%) verification.Only the intraparticle diffusion model fits the experimental data.Thus, it was determined to be the rate limiting step for the initial period of the adsorption process.

Adsorption Isotherms
The plots of the Freundlich and Langmuir isotherm models are presented as Figs.17 and 18, respectively.The isotherm constants and maximum adsorption capacity (q max ) values are listed in Table 6.According to the linear regression method, the formaldehyde adsorption by AC adsorptive filter media exhibits a better fit to Langmuir equation was statistically confirmed by giving greater R 2 values closer to unity (R 2 > 0.987).This denotes that the Langmuir model  may better describe an adsorption isotherm for AC adsorptive filter media.This adsorptive behavior pointed out that the adsorption occurs on a heterogeneous surface, which may be aspect to the various active sites on AC adsorptive filter media.The overall adsorptive performance prevails as a physical adsorption process.This phenomenon has been described before (Cheng and Tsai, 2007;Bernabe et al., 2015).The results show that the maximum formaldehyde adsorption capacity (q max ) of AC adsorptive filter media was 0.7862 mg g -1 at 0.75 m s -1 face velocity.From the observed results we conclude that AC adsorptive filter media is potentially a good solution for formaldehyde removal.
Table 5. Fitting parameters of three kinetic models for formaldehyde adsorption.Face velocity (m s -1 ) Freundlich isotherm Langmuir isotherm K f (mg g -1 )(L mg -1 ) 1/n 1/n R 2 q max (mg g -1 ) K L (L mg Except than the Freundlich and Langmuir isotherms, the experimental data were also represented by the D-R equation.Fig. 19 was plotted as lnW versus A 2 for AC filter from adsorption isotherms of N 2 data of Fig. 3.As shown in the figure, the characteristic curve for formaldehyde is simulated linearly at a lower A 2 range.Nevertheless, the isotherm data of formaldehyde cannot be linearly fitted over the entire range of abscissa.A clear transition was observed at ~2.2 × 10 7 J 2 mol -2 of A 2 , which is equal to a relative pressure (P/Po) of 0.151 for the adsorbates to represent a good fit at lower levels of A 2 (high P/Po) and of a big discrepancy at high A 2 (low P/Po) in agreement with Shiue et al. (2011) research work.The results show that the D-R equation can simulate the experimental adsorption data except very low relative pressures.In the event of relative pressures lower than 0.151, the D-R equation may be difficult to utilize the simulation of the adsorption capacity for the tested adsorption systems.

CONCLUSIONS
According to this study, formaldehyde removal by AC adsorptive filter media is effective in indoor environments.The SEM images showed that AC surface were rather uneven, with coarse and small pores.Irregular layer structures were formed amorphously, and the XRD diffraction peaks were broad.C, O, Mg, P etc. were detected via EDS analysis, which showed that the Mg/C ratio = 0.68% and further proves the existence of MgO in AC.According to BET analysis checked with FTIR, the surface area was 1333.3304m 2 g -1 , and ketone -C=O bonds, which explain the presence of a sensible peak at 3417 cm -1 and weak strength bonding at 2329 cm -1 , were successfully grafted onto the carbon.
The results indicate that an increased initial concentration of formaldehyde and face velocity is associated with a higher adsorption capacity and faster breakthrough time.The breakthrough behavior at low formaldehyde concentrations can be linearly expressed by the relationship between the natural logarithm of the breakthrough time and the natural logarithm of the initial concentration.High correlation coefficients (R 2 > 0.972) for the formaldehyde adsorption onto the coconut activated carbon filter media confirm good agreement between the Yoon-Nelson model and the experimental data.Regarding the adsorption kinetics of formaldehyde removal by AC adsorptive filter media, the pseudo-second-order model displayed the highest correlation coefficient (0.94 < R 2 < 0.984) and lowest MAPE values (8%), demonstrating more accurate prediction than the pseudo-first-order model; the intraparticle diffusion model and membrane diffusion was able to predict the adsorption kinetics.The Langmuir equation is well-fitted to the AC adsorptive filter.The D-R equation successfully predicted the equilibrium capacity of AC to adsorb formaldehyde at high relative pressures.Overestimation of the adsorption capacity was detected when predicting the formaldehyde adsorption capacity at relative pressures below 0.151.

Fig. 10 .
Fig. 10.The relationships between formaldehyde concentrations and breakthrough times.

Fig. 13 .
Fig. 13.The relationship between the Pseudo-first-order rate constant and formaldehyde initial concentration.

Fig. 15 .
Fig. 15.The relationship between the Pseudo-second-order rate constant and formaldehyde initial concentration.
It starts after the above mentioned time schedule at 0.25 to 0.79 ppm inlet formaldehyde concentration of 0.25, 0.5, and 0.75 m s -1 face velocity, respectively.The formaldehyde is slowly removed via intraparticle diffusion into the particles and is finally kept in the micropores.Generally, intraparticle diffusion rate constant k i is the slope of the Stage 2 line.The values of k i arise from 0.031 to 0.049 min -1/2 (0.25 m s -1 ), from 0.041 to 0.089 min -1/2 (0.5 m s -1 ), and from 0.072 to 0.133 min -1/2 (0.75 m s -1 ) of AC adsorptive filter media when increase from 0.25 ppm to 0.79 ppm, respectively.Nevertheless, the linear intercept C is not zero and larger, showing that the membrane diffusion in Stage 3 also affected the adsorption rate(Tang et al., 2016).Three stage of the intraparticle diffusion model fitted the adsorption data well.The formaldehyde adsorption onto AC adsorptive filter media is affected by combined intraparticle diffusion model and membrane diffusion(Tang et al., 2016).

Table 2 .
Correlations of formaldehyde adsorption capacity with time and concentrations.

Table 3 .
The relationships between formaldehyde concentrations and breakthrough times.

Table 4 .
The theoretical parameters k', t, and K.